{
  "id": 5895,
  "curve_key": "2734393185664:-4519678400387447552",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-56966524701",
    "5231128248549261"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 85.91079197168219,
  "faltings_height": 4.902203200096025,
  "conductor": "433654794186311156160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "41",
    "53",
    "73",
    "241",
    "2551",
    "20959"
  ],
  "discriminant": "10016336703215290093853801518080",
  "regulator": "5875671.1623491125724069427850274532055576009614892245860",
  "points": [
    [
      "99293",
      "23530424"
    ],
    [
      "539477/4",
      "-9159083/8"
    ],
    [
      "-195235",
      "94399336"
    ],
    [
      "4329249/25",
      "-2955925332/125"
    ],
    [
      "24432945/169",
      "-9074660148/2197"
    ],
    [
      "5200404/25",
      "-6100892433/125"
    ],
    [
      "2053113/16",
      "373678011/64"
    ],
    [
      "346740",
      "-164822661"
    ],
    [
      "-309564156/1225",
      "-2532543395103/42875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_9.add_2026-10-24.tsv.gz, 1940th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b:\r\nhttps://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_9.add_2026-10-24.tsv.gz\r\n\r\nThe source row reports proven rank 9 with torsion Z/2 and supplies these nine generators on the minimal model. I checked all nine points exactly and independently verified their independence. The torsion subgroup was computed separately. Conductor 433654794186311156160. The construction author and search method are not identified in the source row.",
  "created_at": "2026-10-25 20:19:15",
  "updated_at": "2026-10-25 20:19:15"
}